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National and Regional Contests
Ireland Contests
Ireland National Math Olympiad
2005 Irish Math Olympiad
1
easy
easy
Source: Ireland 2005
July 6, 2009
modular arithmetic
number theory proposed
number theory
Problem Statement
Show that
200
5
2005
2005^{2005}
200
5
2005
is a sum of two perfect squares, but not a sum of two perfect cubes.
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